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Question

A sphere of mass 10 kg is moving on a horizontal plane with a velocity (10^i+^j) m/s where it collides with a vertical wall which is parallel to ^j. If the coefficient of restitution is 0.5, find the impulse (in SI units) acted on the sphere. 
  1. 150 ^i^j
  2. 15 ^i
  3. 150 ^i
  4. 55 ^i+^j


Solution

The correct option is C 150 ^i
Given, velocity of the sphere v=10^i+^j.
The situation is as shown in the below figure.


Momentum of the individual particle will be conserved perpendicular to LOI. Here along ^j (along the vertical wall) momentum of individual particle will be conserved. 

As, e=Velocity of seperationVelocity of approach along LOI
 0.5=0vx100
 vx=5^i where, vx is the speed of sphere after collision, along the xaxis or along the LOI.

Hence, velocity of sphere after collision is
v=5^i+^j
So, impulse on sphere is given by
J=P=mvmu
 J=m[(5^i+^j)(10^i+^j)]=10×[15 ^i]
 J=150 ^i

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